Hille–Nehari theorems for dynamic equations with a time scale independent critical constant

Başak Karpuz

Applied Mathematics and Computation, 2019, vol. 346, issue C, 336-351

Abstract: In this paper, we give Hille–Nehari test for nonoscillation/oscillation of the dynamic equation(rxΔ)Δ(t)+p(t)x(t)=0fort∈[t0,∞)T,where t0∈T,supT=∞,r∈Crd([t0,∞)T,R+) and p∈Crd([t0,∞)T,R0+). We show that the critical constant for this dynamic equation is 14 as in the well-known cases T=R and T=Z. We also present illustrating examples showing that the critical constant 14 is sharp on arbitrary time scales. With two different techniques, we extend our results to the dynamic equation(rxΔ)Δ(t)+p(t)xσ(t)=0fort∈[t0,∞)Tby preserving the constant 14. The second technique is new even for the discrete case T=Z.

Keywords: Hille–Nehari; Oscillation; Nonoscillation; Time scale; Dynamic equation (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:336-351

DOI: 10.1016/j.amc.2018.09.055

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